Rydberg Equation Calculator

1/λ = R·Z²·(1/n₁² − 1/n₂²). For hydrogen R is 1.09678 × 10⁷ m⁻¹ — the reduced-mass-corrected value, not R∞ — and the result is the wavelength emitted or absorbed as an electron moves between levels n₁ and n₂.

Because of where the energies land. Transitions ending on n = 2 happen to fall between 380 and 660 nm — H-alpha at 656 nm is the red line that gives nebulae their colour. Lyman transitions ending on n = 1 are ultraviolet, and Paschen onwards are infrared.

Only for one-electron species: H, He⁺, Li²⁺, Be³⁺. Once there are two electrons they repel each other, and that repulsion is not in the equation. Multi-electron spectra need quantum mechanical calculation.

The wavelength when n₂ goes to infinity — the electron is removed entirely. For the Lyman series that is 91.18 nm, corresponding to hydrogen's 13.6 eV ionisation energy.

Because that is the wavelength in air. These are vacuum wavelengths, and air's refractive index shortens visible light by about 0.03%. Vacuum 656.47 nm and air 656.28 nm are the same line.